Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Number problems at primary level that require careful consideration.
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.
On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
Woof is a big dog. Yap is a little dog. Emma has 16 dog biscuits to give to the two dogs. She gave Woof 4 more biscuits than Yap. How many biscuits did each dog get?
There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?
Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?
A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.
The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
There were 22 legs creeping across the web. How many flies? How many spiders?
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
Claire thinks she has the most sports cards in her album. "I have 12 pages with 2 cards on each page", says Claire. Ross counts his cards. "No! I have 3 cards on each of my pages and there are. . . .
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Can you score 100 by throwing rings on this board? Is there more than way to do it?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?
Are these domino games fair? Can you explain why or why not?
How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?
Can you substitute numbers for the letters in these sums?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
Sam got into an elevator. He went down five floors, up six floors, down seven floors, then got out on the second floor. On what floor did he get on?
Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?
Use the number weights to find different ways of balancing the equaliser.
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Number problems at primary level to work on with others.
Got It game for an adult and child. How can you play so that you know you will always win?
A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.
If you have only four weights, where could you place them in order to balance this equaliser?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
This dice train has been made using specific rules. How many different trains can you make?
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
Can you hang weights in the right place to make the equaliser balance?
Number problems at primary level that may require determination.
Who said that adding couldn't be fun?
Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
An environment which simulates working with Cuisenaire rods.
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.
Noah saw 12 legs walk by into the Ark. How many creatures did he see?